A mixture model (mixture distributions) for representing data using a plurality of models is important in industrial applications. There are various examples thereof such as a mixture normal distribution model and a mixture hidden Markov model. For example, such a mixture model is industrially used for finding a dishonest medical bill based on an observed outlier (Non Patent Literature 1) or detecting a network failure (Non Patent Literature 2). In addition, other important application examples of mixture models include customer behavior clustering in marketing (study on the assumption that similar customers belong to the same model) and analysis on topics of articles (study on the assumption that articles of the same topic belong to the same model).
Generally, in the case where the number of mixture (mixture number) of a plurality of models constituting a mixture model (also called components) and the types of components are specified, well-known methods such as an EM algorithm (Non Patent Literature 3) and a variational Bayesian method (Non Patent Literature 4) can be used to specify parameters of distributions (models). It is necessary to determine a mixture number and component types for estimating such parameters. The issue of specifying such models is generally called “model selection issue” or “system identification issue,” and considered as an important issue for constructing reliable models. Therefore, many techniques relating to the issue have been proposed.
For example, methods of selecting a model that has a maximum posterior probability are known as methods for determining the number of models to be mixed. Methods proposed for that purpose are: 1) a method based on the amount of Bayesian information; 2) a method based on a variational Bayesian method (for example, Non Patent Literature 4); 3) a method based on nonparametric Bayesian estimation using a Dirichlet process (for example, Non Patent Literature 5); etc.